You are building a design matrix for a linear model. The categorical feature city has three levels (A, B, C) and has been one-hot encoded into three columns. Alongside it sit a scaled numeric feature age and the usual bias column of all ones. Six training rows:
| bias | city_A | city_B | city_C | age |
|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 2 |
| 1 | 1 | 0 | 0 | 4 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 3 |
| 1 | 0 | 0 | 1 | 5 |
| 1 | 0 | 0 | 1 | 0 |
Read each of the columns as a vector in . What is the dimension of the subspace of that these five columns span (the column space of the design matrix)?
Select all that apply.